Question

A plano convex lens fits exactly into a plano concave lens. Their plane surface are parallel to each other. If the refractive indices are ${\mu }_1$ and ${\mu }_2$ and R is the radius of curvature the focal length of the combination is

• A. $\frac{R}{{\mu }_1-{\mu }_2}$
• B. $\frac{2R}{{\mu }_2-{\mu }_1}$
• C. $\frac{R}{2({\mu }_1-{\mu }_2)}$
• D. $\frac{R}{2-({\mu }_1-{\mu }_2)}$

Answer 1

The correct option is A $\frac{R}{{\mu }_1-{\mu }_2}$

$\frac{1}{F}=\frac{1}{f_1}-\frac{1}{f_2}=\frac{({\mu }_1-1)1}{R}-({\mu }_2-1)\frac{1}{R}\frac{1}{F}=\frac{{\mu }_1-{\mu }_2}{R}F=\frac{R}{{\mu }_1-{\mu }_2}$